LaTeX
\neg(p\land q)\equiv(\neg p)\lor(\neg q)Variables
- p, q: propositions
- ¬: logical negation
- ∧, ∨: conjunction and disjunction
How to use this formula
Rewrites the negation of a conjunction as a disjunction of negations.
Important notes
- The dual law negates a disjunction into a conjunction.
- The equivalence holds for classical Boolean logic.
Quick example
“Not both conditions hold” is equivalent to “at least one condition fails.”
Applicability, worked calculation, and verification
Assumptions and domain checks
- The dual law negates a disjunction into a conjunction.
- State the logical system, operator precedence, and whether equivalence is semantic, syntactic, or truth-functional.
Worked example
“Not both conditions hold” is equivalent to “at least one condition fails.”
Common mistakes
- Before substituting values into De Morgan Law for Logic, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Verify the result of De Morgan Law for Logic with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use De Morgan Law for Logic in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\neg(p\land q)\equiv(\neg p)\lor(\neg q). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the De Morgan Law for Logic used for?
Rewrites the negation of a conjunction as a disjunction of negations.
Can I copy this formula as LaTeX?
Yes. Copy \neg(p\land q)\equiv(\neg p)\lor(\neg q) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.